FP3 locus problem

The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
x=16m/(1+4m²)
y=-2/(1+4m²)

b) As m varies, find in cartesian form, an equation of the locus of M
Stuck on this one.

The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
x=16m/(1+4m²)
y=-2/(1+4m²)

b) As m varies, find in cartesian form, an equation of the locus of M
Stuck on this one.

As you see from the coordinates of the M

x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)

As you see from the coordinates of the M

x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)

Which line? I get an ellipse.

I get $x= \frac{8m}{1+4m^2}$ so one of us seems to be a factor of 2 out. I agree with the expression for $y$



You have to eliminate $m$ between the expressions that you have for $x,y$ to find an equation for the locus in terms of $x,y$.